stripe shader no uv unwrapping
One way to get stripes is to use a 'Checker Texture' and use a 'Mapping' node to stretch the texture in one axis. Of course this would only produce a two-color striped texture and it appears that you want a multi-colored texture. In that case I think you could layer some 'Checker Textures' using Alpha and offsetting their mapping coordinates. I'll give it a try to see if it's a viable solution and let you know how it goes.

This seems to work (if I understand your question correctly). You would have to play with the values to achieve the thin black line.